The equation of the logarithmic spiral is:

**r = e^aθ**

Where

**r**is is the radius,

**e**is Euler's number,

**a**is a constant and

**θ**is the angle.

Note that eqaution of the form

**y=e^x**is equal to its own derivative. Its rate of change is not calculable. You may ask what the radius

**r**pertains to. All motion must have and center that is unmoving. This is the universal frame of reference and that center lies outside of space-time.

Since I live in South Florida I like to use the hurricane and the seashell as examples of the spiral motion. Astronomers may look at the spiral galaxies. Those who are constipated may relate to the spiral of the toilet flush. haha.

This eqaution remains the same under various geometric transformations such as

**inversion.**To graph

**r**as

**1/r**merely produces the mirror image of the same spiral. This is akin to viewing the Earth from the South pole instead of the North pole.

The

**evolute**of of the logartihmic spiral produces the same spiral. The

**cycloid**also has this property. A close look at the cycloid reveals that it traces out half of an ellipse at each cycle. No one has ever noticed this before. The ellipse is also a very identifiable natural motion of every orbit ever observed since Kepler. The elliptical orbit is a spiral motion!

This finally solves the mystery of motion and explains why we cannot get a grip on it. Mathematics is useless. The calculus was good enough for approximation up until we wanted to penetrate the vastness of space, the macrocosmos. It is a perpetual problem at the quantum level. At these extremes all breaks down because motion is not calculable. Computation has been able to get us into space but we cannot stay there too long. Gravity always wins out in the end. Our computers cannot compute to infinite digits.